Two integers x and y are chosen with replacement from the set [0,1,2,3, , 10].

Question

Two integers $x$ and $y$ are chosen with replacement from the set $$\{0,1,2,3, \ldots, 10\}$$. Then the probability that $|x-y|>5$, is :

Accepted Answer

If $x=0, y=6,7,8,9,10$

If $x=1, y=7,8,9,10$

If $x=2, y=8,9,10$

If $x=3, y=9,10$

If $x=4, y=10$

If $x=5, y=$ no possible value

Total possible ways $$=(5+4+3+2+1) \times 2$$

$=30$

Required probability $$=\frac{30}{11 \times 11}=\frac{30}{121}$$

Solutions · 1